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Vlad [161]
3 years ago
12

Find a formula for the inverse of the function f(x)=3x^3 + 2sinx + 4cosx

Mathematics
1 answer:
vitfil [10]3 years ago
5 0
Explicit Functiony = f(x) is said to define y explicitly as a function of x because the variable y appears alone on one side of the equation and does not appear at all on the other side. (ex. y = -3x + 5)Implicit FunctionAn equation in which y is not alone on one side. (ex. 3x + y = 5)Implicit DifferentiationGiven a relation of x and y, find dy/dx algebraically.d/dx ln(x)1/xd/dx logb(x) (base b)1/xln(b)d/dx ln(u)1/u × du/dxd/dx logb(u) (base b)1/uln(b) × du/dx(f⁻¹)'(x) = 1/(f'(f⁻¹(x))) iff is a differentiable and one-to-one functiondy/dx = 1/(dx/dy) ify = is a differentiable and one-to-one functiond/dx (b∧x)b∧x × ln(b)d/dx e∧xe∧xd/dx (b∧u)b∧u × ln(b) du/dxd/dx (e∧u)e∧u du/dxDerivatives of inverse trig functionsStrategy for Solving Related Rates Problems<span>1. Assign letters to all quantities that vary with time and any others that seem relevant to the problem. Give a definition for each letter.

2. Identify the rates of change that are known and the rate of change that is to be found. Interpret each rate as a derivative.

3. Find an equation that relates the variables whose rates of change were identified in Step 2. To do this, it will often be helpful to draw an appropriately labeled figure that illustrates the relationship.

4. Differentiate both sides of the equation obtained in Step 3 with respect to time to produce a relationship between the known rates of change and the unknown rate of change.

5. After completing Step 4, substitute all known values for the rates of change and the variables, and then solve for the unknown rate of change.</span>Local Linear Approximation formula<span>f(x) ≈ f(x₀) + f'(x₀)(x - x₀)
f(x₀ + ∆x) ≈ f(x₀) + f'(x₀)∆x when ∆x = x - x₀</span>Local Linear Approximation from the Differential Point of View∆y ≈ f'(x)dx = dyError Propagation Variables<span>x₀ is the exact value of the quantity being measured
y₀ = f(x₀) is the exact value of the quantity being computed
x is the measured value of x₀
y = f(x) is the computed value of y</span>L'Hopital's RuleApplying L'Hopital's Rule<span>1. Check that the limit of f(x)/g(x) is an indeterminate form of type 0/0.
2. Differentiate f and g separately.
3. Find the limit of f'(x)/g'(x). If the limit is finite, +∞, or -∞, then it is equal to the limit of f(x)/g(x).</span>
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Please please answer this correctly. Please take a pic of the same screenshot of put the right plots correctly
sergeinik [125]

Answer:

Picture

Step-by-step explanation:

I graphed them

4 0
3 years ago
Please help me i am desperate please (1/3)
Sergeu [11.5K]

I think we're not supposed to do more than 3 problems in one answer; certainly not five pages. Does the 1/3 mean there are 10 more to come?

I'll do the first page.

6)

Right triangle, opposite side of 10, adjacent side of 21,

tan x = opp/adj = 10/21

x = arctan 10/21 = 25.46°

Answer: 25

7)

cos x =   adj / hyp = 10/14

x = arccos 10/14 = 44.42°

Answer: 44

8)

tan x = opp/adj = 12/24 = 1/2

x = arctan 1/2 = 26.57°

Answer: 27

9)

tan x = 31/32

x = arctan 31/32 = 44.09°

Answer: 44

10)

x = arctan 10/27 = 20.32°

Answer: 20

8 0
3 years ago
If a coin is flipped twenty-five times and lands tails up seventeen times, the experimental probability that the coin lands tail
aliina [53]
Tails was landed 17/25 times, so the experimental probability would be .68 or 68%
17/25 = .68
Hope this helps!
5 0
3 years ago
Why do you need axioms in theorems? <br>​
mihalych1998 [28]

Axioms serve as the starting point of other mathematical statements. These statements, which are derived from axioms, are called theorems. A theorem, by definition, is a statement proven based on axioms, other theorems, and some set of logical connectives.

<h3>Hope it helps...</h3>
7 0
2 years ago
Find the vertex of the function f(x) = x2 - 8x + 15.
defon

Answer: (4, -1)

Step-by-step explanation: You have to rewrite in vertex form and use the form to find the vertex

7 0
3 years ago
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